**4.4 Math minibooks**

We had initially prototyped math minibooks that were bilingual in English and Spanish on each page. These eight-page, easy-to-read books were printed in black and white and could be easily printed and assembled at home or by teachers to be sent home with children. The minibooks were designed to complement the math games and give families a fun way to help their children deepen their learning by reading the books together and practicing the math concepts at home. Families told us how much they liked having English and Spanish on the same page and this also helped teachers who could send the same resources home to families whose home language was either Spanish or English. While this was valued by teachers and families, they also asked for additional versions that included more languages. We worked to add Portuguese and Arabic to these resources.

### **4.5 Families want to learn about young children's mathematical development**

At first, we thought that families would not want to learn as much about children's mathematical development as teachers need to know. But we were wrong. The families who participated in our studies were clear that they wanted to know about the research in early mathematics and children's learning trajectories. Therefore, all of the written and video game directions include information about the mathematics children are learning, including common misconceptions and ways to extend their learning.

#### **4.6 Math lens**

Teachers and families emphasized that the games were a launching point for them to begin to see the world through a math lens and to develop that math lens in their children. Teachers and families alike reported that children not only asked to play the YM math games, but they also began creating their own math games.
